Find the points of intersection for f(x) = 3x – 1 and g(x) = (x – 1)^2 + 2 . I don't even know where to start on this one, someone help?

Question

Find the points of intersection for f(x) = 3x – 1 and g(x) = (x – 1)^2 + 2 .  I don't even know where to start on this one, someone help?

3mar · Answer

May I help?

tkhunny · Answer

Plot on the same set of coordinate axes and see if something to do becomes more obvious.

y = 3x – 1 and y = (x – 1)^2 + 2

bluestar70556 · Answer

@3mar Sure!
@tkhunny If I graph them together it shows that they intersect at two points.  But I want to be able to show my work, do I need to use the quadratic formula?

tkhunny · Answer

I don't actually want you to graph them.  Just look at the new formulas if we were to attempt that.  Both of those expressions in 'x' are equal to the same 'y'.  This shoudl suggest the equality of the two expressions.

It is possible that you will need the Quadratic Formula.

bluestar70556 · Answer

So we can say that technically they are equal to each other at some point.  That being said:

$$x^2-2x+3 = 3x - 1$$

Which can also be simplified to:

$$x^2 - 5x + 4$$ Correct?

tkhunny · Answer

f(x) = g(x) may have been clear enough.  I thought it might be more obvious if I set them both equal to y.  You seem almost to have the idea.  Put the "=0" back in there and solve away!  You won't need the Quadratic Formula.

bluestar70556 · Answer

Okay I see now!

I can factor out the equation which will give me:

(x - 1)(x - 4) = 0

So my x values are 1 and 4, NOW I can go back to my equation and plug in x to figure out my y's, thanks for your help! ^-^

tkhunny · Answer

Good work.  :-)